This book is the first book on Toeplitz iterative solvers and it includes recent research results.The author belongs to one of the most important groups in the field of structured matrix computation.The book is accessible to readers with a working knowledge of numerical linear algebra.It should be of interest to everyone who deals with block Toeplitz systems,numerical linear algebra,partial defferential equations,ordinary differential equations,image processing and approximation theory.
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目录
Preface Chapter 1 Introduciton 1.1 Background 1.2 Circulant preconditioners 1.3 Non-circulant preconditioners Chapter 2 Block Circulant Preconditioners 2.1 Operators for block matrices 2.2 Operation cost for preconditioned system 2.3 Convergence rate 2.4 Invertibility of r(2)F,F(Tmm)and s(2)F,F(Tmm) 2.5 Numerical results Chapter 3 BCCB Preconditioners from Kernels 3.1 Introduction 3.2 Preconditioners from kernels 3.3 Clustering properties Chapter 4 Fast Algorithm for Tensor Structure 4.1 Construction of preconditioner 4.2 Fast algorithm 4.3 Inverse heat problem 4.4 Numerical results Chapter 5 Block Toeplitz LS Problems 5.1 Introduction 5.2 Construction of preconditioner 5.3 Spectrum of preconditioned matrix 5.4 Convergence rate and operation cost Chapter 6 Block {ω}-Circulant Preconditioners 6.1 Spectral analysis 6.2 Construction of preconditioner 6.3 Clustering of eigenvalues 6.4 Numerical results Chapter 7 Non-Circulant Block Preconditioners 7.1 Block band Toeplitz preconditioners 7.2 Preconditioners based on fast transforms Chapter 8 Multigrid Block Toeplitz Solvers 8.1 Introduction 8.2 Convergence rate of TGM 8.3 Convergence result for full MGM 8.4 Numerical results Chapter9 Applications in Second-Order PDEs 9.1 Applications to elliptic problems 9.2 Applications to hyperbolic problems 9.3 Extension to parabolic equations 9.4 Numerical results 9.5 3-dimensional problems Chapter 10 Applications in First-Order PDEs 10.1 Discretized system and GMRES method 10.2 Construction of preconditioner 10.3 Convergence rate 10.4 Spectral analysis 10.5 Asymptotic properties 10.6 Convergence results and numerical tests Chapter 11 Applications in ODEs and DAEs 11.1 BVMs and their matrix forms 11.2 Construction of preconditioner 11.3 Convergence rate and operation cost 11.4 Algorithm for DAEs 11.5 Numerical results Chapter 12 Applications in Image Processing 12.1 Introduction 12.2 Regularized PCGLS method 12.3 Numerical results Bibliography Index
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